Autumn 2021
Meeting:
MWF 11:30am - 12:20pm / SIG 225
SLN:
18167
Section Type:
Lecture
Instructor:
Minseon Shin
NO OVERLOADS
CONTENT WILL INCLUDE:
ELEMENTARY THEORY OF RINGS AND
FIELDS: POLYNOMIAL RINGS. IDEALS,
HOMOMORPHISMS, QUOTIENTS, AND
FUNDAMENTAL ISOMOROPHISM
THEOREMS.
FIELDS AND MAXIMAL IDEALS.
EUCLIDEA
RINGS. FIELD EXTENSIONS. ALGEBRAIC
EXTENSIONS. VECTOR SPACES AND
DEGREES OF EXTENSIONS. ADJOINING
ROOTS OF POLYNOMIALS. FINITE
FIELDS
STRAIGHT EDGE AND COMPASS
CONSTRUCTIONS.
Catalog Description:
Elementary theory of rings and fields: basic number theory of the integers, congruence of integers and modular arithmetic, basic examples of commutative and non-commutative rings, an in depth discussion of polynomial rings, irreducibility of polynomials, polynomial congruence rings, ideals, quotient rings, isomorphism theorems. Additional topics including Euclidean rings, principal ideal domains and unique factorization domains may be covered. Course overlaps with: MATH 411; MATH 412; and STMATH 403. Prerequisite: either a minimum grade of 2.0 in MATH 300 and a minimum grade of 2.0 in either MATH 208 or MATH 308, a minimum grade of 2.0 in MATH 334, or a minimum grade of 2.0 in MATH 136 and a minimum grade of 2.0 in MATH 300. Offered: AWS.
GE Requirements Met:
Natural Sciences (NSc)
Credits:
3.0
Status:
Active
Last updated:
October 11, 2024 - 12:00 pm